Question

The 12th term of an arithmetic sequence is
25 and the common difference is 3. What
is the 17th term?​

Answer 1

✬ 17th Term = 40 ✬

Step-by-step explanation:

Given:

• 12th term of an AP is 25.
• Common difference is 3.

To Find:

• What is the 17th term ?

Solution: As we know that the nth term of an AP is given by

★ aⁿ = a + (n – 1)d ★

• a = first term
• d = common difference
• n = number of terms

A/q

• 12th term of an AP is 25.

➟ a¹² = a + (n – 1)d

➟ 25 = a + (12 – 1)3

➟ 25 = a + 11 × 3

➟ 25 = a + 33

➟ 25 – 33 = a

➟ – 8 = a

So we got first term of AP i.e –8.

Let's find the 17th term.

➟ a¹⁷ = a + (n – 1)d

➟ a¹⁷ = –8 + (17 – 1)3

➟ a¹⁷ = –8 + 16 × 3

➟ a¹⁷ = – 8 + 48

➟ a¹⁷ = 40

Hence, 17th term of Arithmetic sequence is 40.

Answer 2

$\Large \underline{ \underline{ \bf \purple{Given :}}}$

• 12th termof A.P = 25

• Common difference = 3

$\Large \underline{ \underline{ \bf \purple{To \: Find :}}}$

• 17th term of the given A.P

$\Large \underline{ \underline{ \bf \purple{Solution :}}}$

$\longrightarrow \sf A_{12} = a + 11d \\ \\\longrightarrow \sf 25 = a + 11 \times 3 \\ \\\longrightarrow \sf 25 = a + 33 \\ \\\longrightarrow \sf a = 25 - 33 \\ \\\longrightarrow \underline{\boxed{ \sf a = - 8}}$

Now , 17th term of the A.P

$\longrightarrow \sf A_{17} = a + 16d \\ \\\longrightarrow \sf A_{17} = - 8 + 16 \times 3 \\ \\\longrightarrow \sf A_{17} = - 8 + 48 \\ \\ \longrightarrow \underline{ \boxed{ \sf \orange{A_{17} =40}}}$

$\large\underline{ \green{\bf \therefore 17th \: term \: of \: A.P = 40}}$